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Given a set V of m vectors (points in R^n), the Gram matrix G is the matrix of all possible inner products of V, i.e., g_(ij)=v_i^(T)v_j. where A^(T) denotes the transpose. ...

The kernel of a group homomorphism f:G-->G^' is the set of all elements of G which are mapped to the identity element of G^'. The kernel is a normal subgroup of G, and always ...

Let u_1<=u_2<=... be harmonic functions on a connected open set U subset= C. Then either u_j->infty uniformly on compact sets or there is a finite-values harmonic function u ...

Let K be a number field with ring of integers R and let A be a nontrivial ideal of R. Then the ideal class of A, denoted [A], is the set of fractional ideals B such that ...

Conditions at an initial time t=t_0 from which a given set of mathematical equations or physical system evolves. A system with initial conditions specified is known as an ...

Let S={x_1,...,x_n} be a set of n distinct positive integers. Then the matrix [S]_n having the least common multiple LCM(x_i,x_j) of x_i and x_j as its i,jth entry is called ...

L=sigma/(sigma_B), where sigma is the variance in a set of s Lexis trials and sigma_B is the variance assuming Bernoulli trials. If L<1, the trials are said to be subnormal, ...

Pathological functions that are continuous but differentiable only on a set of points of measure zero are sometimes known as monsters of real analysis. Examples include the ...

A theorem in game theory which guarantees the existence of a set of mixed strategies for finite, noncooperative games of two or more players in which no player can improve ...

The set of nilpotent elements in a commutative ring is an ideal, and it is called the nilradical. Another equivalent description is that it is the intersection of the prime ...